Nomenclature

A	cross-sectional flow area of a pipe
c_p	specific heat, constant pressure
C_D	discharge coefficient
C_V	valve coefficient
CHW	Hazen-Williams factor
D	diameter of a pipe
f	friction factor
f_T	turbulent friction factor (used by Crane, 1988Crane Co., Flow of Fluids Through Valves, Fittings, and Pipe, Technical Paper No. 410, Crane Co., Joliet, IL, 1988.)
f_L	laminar friction factor
f_Tr	transition friction factor
F	error value in mass balance
Fr	Froude number
g	gravitational constant
h	convection coefficient
h	enthalpy
H	head
HGL	hydraulic gradeline (same as head)
J	Jacobian matrix
k	thermal conductivity
K	loss factor
K	constant for Power Law fluid
K_sprinkler	fire sprinkler loss factor
L	length of a pipe
ṁ	mass flow rate
n	general constant
n	constant for Power Law fluid
Nu	Nusselt Number
P	pressure, static
P_h	heated perimeter
P_o	pressure, stagnation
P_w	wetted perimeter
q	heat rate to a pipe
Q	volumetric flow rate
q"	heat flux
r	radius
r	relaxation
R, R’	resistance
R_c	coefficient of rigidity
Re	Reynolds Number
R_h	Hydraulic radius (equal to radius divided by 2)
s	pump speed
S	Submergence
S	Hydraulic gradeline gradient
S_y	yield stress
T	temperature
U	overall heat transfer coefficient
V	velocity
x	distance along pipe centerline
z	elevation
a, m, q	angle
b	diameter ratio
e	roughness
n	kinematic viscosity
ρ	density
μ	dynamic viscosity

Subscripts

i	junction at which solution is sought
j	junctions with pipes connecting to junction i
o	stagnation
∞	infinity, far away, ambient